Triangles FIM and LAK below are similar with $\displaystyle{m}\angle{A}={m}\angle{I}\usepackage{cmbright}\Huge\$ and $\displaystyle{m}\angle{K}={m}\angle{M}\usepackage{cmbright}\Huge\$ .

What is the length of $\displaystyle{\overline{{{L}{A}}}}\usepackage{cmbright}\Huge\$ ?